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rh : f) x IR---+ IR une fonction continue et une suite up ? (r On considère la suiae de fonctions l:(r,up(ae)) Si z1 converge vers u et t[(.,ur(.)) converge vers y'-, alors en gên&al t!' + tb(.,r(.)). [a notion de mesures de Young associée à u6 va nous perrnettre d'exprimer dl. Avant d'énoncer le théorème d'existence des mesures de Young, rappelons quelque.s résultats d'analyse fonctionnelle. L'espace co(IR,-): {.f e c(IR-) : r^tl, o} est un espace de Banach pour la nolme de la convergence uniforme. Son espace dual est I'espace des mesure.s de Radon noté ilr'(IR-) muni de la norme llPllnzrm-y: hl(R-) ,
IR-) est séparable on a : (lt(ç1 ,
1 tr,l; r: I tg@, IR-)) et p e trf.(C), l/(IR*)) où -Lf ,
il4(IR-)) est llpll : sup essr?ollp"llrrrIR-i ,
tls : f) x IR---IR, une fonction ile Carathéod,ory et u6: O -* IR-u,ne suite ile fonctions rnesurable-s tellc qu,e: l"r(')l <Cp.p. r?f)Vk ,